The modeling of real-world systems through mathematics has been utilized to determine how systems response to real-world inputs. Due to the nature of such modeling, computers are often used to assist in such modeling. The modeling of liquid and gas flow in piping network presents a situation in which the more detailed the piping network, the more difficult it is to model such piping network, and in most cases, the model does not correlate accurately with real-world piping networks. One area of modeling in piping network is the determination of the location of the liquid front as the liquid moves through the piping that was previously occupied by another liquid or gas. Where the liquid is moving through a single uniform straight pipe, it is believed that an accurate model, i.e., an analytical model, of the characteristics of the liquid can be obtained. Where a movement of the liquid is initiated at some point in a large network of branching pipes so that the liquid flows through the network thereafter, it is believed that the current analytical models are inadequate for such type of complex networks.
These complex piping networks are utilized in the fire protection industry, and, in particular for providing a sprinkler system. In certain sprinkler systems, the pipe is filed with a gas and liquid enters the piping network once the gas is expelled from the piping network by actuation of a sprinkler. These pipe networks are known as “dry pipe” sprinkler systems. Dry pipe sprinkler systems are utilized in areas that are unheated and that are subjected to freezing temperatures. In contrast to a ‘standard’ wet sprinkler system in which the pipes supplying sprinklers are refilled with water under constant pressure, the sprinkler piping for a dry system is, preferably, filled with air under pressure. The air pressure in the system holds a dry pipe valve closed, and the valve opens with a loss of air pressure in the system. The actuation of one or more sprinklers will allow air to escape the piping network and result in the tripping of the dry pipe valve and the filling of the piping network with water (to the sprinklers). By nature, a dry sprinkler system is slower to respond to fire conditions than a wet system because the air must first be exhausted from the system.
It would be advantageous to those individuals who utilize dry pipe sprinkler systems to accurately model the performance of dry pipe sprinkler systems. Currently, these individuals are required to demonstrate certain physical characteristics of the dry pipe system as a function of time by a physical test of an actual system, where the actual system has a volume capacity greater than 750 gallons and in certain cases where the system volume is greater than 500 gallons as set forth in National Fire Protection Association (“NFPA”) in NFPA 13 “The Standard for the Installation of Sprinkler Systems,” 2002 Edition, which is hereby in its entirety incorporated by reference. Rather than testing, individuals would benefit from a model of a dry pipe sprinkler system that could provide characteristics such as, for example, the evacuation of the air from a dry system upon actuation or the tripping of a dry pipe valve, the location of the flow front of the liquid through the system, and the respective time required to do so.
It is believed, however, that these individuals do not have a technique of modeling a dry pipe sprinkler system in manner to accurately predict the characteristics of such dry pipe systems in lieu of an actual test. As a result, it is believed, that these individuals often restrict the system size on the basis of the volume of air that is trapped in the system to avoid any type of actual testing. For example, NFPA 13 provides for certain dry pipe sprinkler systems to be installed without testing. On the other hand, assuming NFPA 13 is the governing standard for the sprinkler system, if such individuals elect to install a system and it fails the required actual testing, the individuals would have to modify or re-design and re-install the system to conform within the requirements of NFPA 13.
As a result of the possibility of failing the required performance test, individuals tend to develop systems smaller than the maximum system that could be utilized. These smaller systems would be selected so that they fall within the category of NFPA 13 of system that can be installed without performance testing. The result is that many systems in unheated warehouses, for example, that could cover a maximum of 40,000 square feet are restricted to 25,000 to 30,000 square feet on the basis of the volume limitation. This results in multiple systems being installed when fewer systems could conceivably be used. In addition, the NFPA restrictions do not recognize variations in supply pressure—a higher supply pressure will permit a higher liquid flow rate and velocity and hence assist in exhausting (or pushing) the air out of a system more quickly than would a lower pressure. Consequently, it is believed that all systems are penalized for the avoidance of the actual testing requirement, and out of the fear of failing the test after the systems are installed.
In addition, the performance of a test introduces water into the piping system. Following the test, the water is drained from the system prior to re-introducing air pressure. Often, water is trapped within the pipes and causes freezing problems after the system is put into service. Another effect of introducing water into the piping network, draining it, and filling the system with air is that any residual moisture can settle and cause premature corrosion within the steel pipe. Hence, it is desirable to avoid actual testings.
Individuals have developed a model to predict time-based characteristics of the dry pipe systems. It is believed that this known model required individuals to convert a dry pipe system under evaluation into a fixed framework or topology dictated by the model. That is, regardless of the actual design, in order to model the design, the actual design must be “translated” into the fixed topology in order for modeling to be performed. This fixed topology model, however, fails to take into account the behavior and characteristics of liquid, gas with liquid and gas flow at every point through every pipe in a dry pipe design.
In particular, as set forth in Factory Mutual Research Corporation (“FMRC”) Document Index No. OTOR8.RA, October, 1993, FMRC provides for the known fixed topology model that fixes a test sprinkler head on the same branch regardless of where in the actual design the test sprinkler would be the one hydraulically farthest from the dry pipe valve would be located; and the riser is fixed to the middle of a cross main piping regardless of where such riser is to be placed in an actual design. The known model is believed to be unreliable because of the forced translation from the arbitrary design into the fixed topology of known model. In addition to requiring a forced translation, the known model summarizes (i.e., “lumps”) all branch lines before and after a main feed line (i.e., “Feed Main”) as respective volumes instead of accounting for liquid flow, gas flow and liquid-gas flow behavior in each pipe.
The known model, in utilizing a forced translation and lumped volumes, provided predictive values for liquid flow that are believed to be higher than a suitable threshold for individuals (e.g., engineer, architects, planners, contractors and jurisdictional authorities) to rely upon. As such, the known model may provide a generalized technique to analyze dry pipe systems but does not account for flow through each pipe so that individuals can use the predictive results with a suitable degree of accuracy.